Aircraft: CHALLENGER 300
Phase of flight: Cruise
Anomaly: Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Clearance; Deviation / Discrepancy - Procedural Published Material / Policy; Inflight Event / Encounter Weather / Turbulence

We were level at approximately 15;000 ft. (unsure of altitude) shortly after departure from ZZZ as we planned a weather divert to ZZZ1. We were IMC with ice detected CAS message and both engine and wing anti-ice on. We began to experience low rumbles and vibrations from the engine(s) followed by L and R Engine Vibration CAS messages. I tried slightly reducing thrust followed by slightly increasing thrust on each engine independently as it wasn't clear from CAS messages which side the problem emanated from. The vibration didn't immediately subside after adjustments to either engine. We then had several CAS messages followed by our PFDs losing all attitude and heading information; in addition to the loss of yaw damper and AP. I don't recall all of the CAS messages but those I remember include: L and R Engine Vibration; EFIS Comparator Inop; Yaw Damper Fail; L Fire Det Fail; FD 1 Fail; as well as red FD; ATT; and HDG flags on both PDFs. I then shifted to using the standby instrument and continued to climb above our cleared altitude as I chose to gain altitude while we still had both engines operative. Given the uncertainty of the failures and being IMC in the mountains I wanted altitude on our side. The PM (Pilot Monitoring) notified ATC of the issue and we were given block altitudes and heading vectors. When we notified ATC of our failures and reliance on the whiskey compass they provided no-gyro vectors. We discussed diversion alternatives and determined that we needed a suitable airport that was VMC. Flying an instrument approach wouldn't be an option. ATC assigned priority handling for us. We got a series of block altitudes and requested different blocks/vectors to stay VMC on top while we determined a course of action. ATC offered ZZZ2 which we accepted and took a turn toward. Shortly thereafter; ATC offered ZZZ3 as a better alternative as it had less terrain and we could stay in their radar control the whole way down. It was only an additional 25 NM to ZZZ3 than ZZZ2 and it was the safer option so we took the clearance/vectors to ZZZ3. We got a series of no-gyro vectors and descents to ZZZ2. I continued to fly with reference to the standby instrument and compass. The PM continued to work the radio and run QRH checklists. It was difficult to determine which checklists to use as there were so many different; seemingly unrelated CAS messages associated with the failures. The engines seemed to operate normally although once during the descent in IMC and icing conditions; the low rumble/vibration returned momentarily. We eventually got vectored straight to the airport and became VMC approximately 10 miles out and 8;000 ft. MSL. Pattern altitude was 6000 MSL. We then made an uneventful visual approach and landing. We were level at approximately 15;000 ft. (unsure of altitude) shortly after departure from ZZZ as we planned a weather divert to ZZZ1. We were IMC with ice detected CAS message and both engine and wing anti-ice on. We began to experience low rumbles and vibrations from the engine(s) followed by L and R Engine Vibration CAS messages. I tried slightly reducing thrust followed by slightly increasing thrust on each engine independently as it wasn't clear from CAS messages which side the problem emanated from. The vibration didn't immediately subside after adjustments to either engine. We then had several CAS messages followed by our PFDs losing all attitude and heading information; in addition to the loss of yaw damper and AP. I don't recall all of the CAS messages but those I remember include: L and R Engine Vibration; EFIS Comparator Inop; Yaw Damper Fail; L Fire Det Fail; FD 1 Fail; as well as red FD; ATT; and HDG flags on both PDFs. The FO (First Officer) who was Pilot Flying then shifted to using the standby instrument and continued to climb above our cleared altitude as I chose to gain altitude while we still had both engines operative. Given the uncertainty of the failures and being IMC in the mountains we wanted altitude on our side. I then notified ATC of the issue and we were given block altitudes and heading vectors. When we notified ATC of our failures and reliance on the whiskey compass they provided no-gyro vectors. We discussed diversion alternatives and determined that we needed a suitable airport that was VMC. Flying an instrument approach wouldn't be an option. ATC gave us priority handling. We got a series of block altitudes and requested different blocks/vectors to stay VMC on top while we determined a course of action. ATC offered ZZZ2 which we accepted and took a turn toward. Shortly thereafter; ATC offered ZZZ3 as a better alternative as it had less terrain and we could stay in their radar control the whole way down. It was only an additional 25 NM to ZZZ3 than ZZZ2 and it was the safer option so we took the clearance/vectors to ZZZ3. We got a series of no-gyro vectors and descents to ZZZ2. I continued to fly with reference to the standby instrument and compass. The PM (Pilot Monitoring) continued to work the radio and run QRH checklists. It was difficult to determine which checklists to use as there were so many different; seemingly unrelated CAS messages associated with the failures. The engines seemed to operate normally although once during the descent in IMC and icing conditions; the low rumble/vibration returned momentarily. We eventually got vectored straight to the airport and became VMC approximately 10 miles out and 8;000 ft MSL. Pattern altitude was 6;000 ft MSL. We then made an uneventful visual approach and landing.I think ice accumulation caused both engines to vibrate. The severity of the vibration led to multiple equipment failures. Flight Crew reported diverting after encountering engine vibrations severe enough to cause multiple systems failures. Flight Crew reported ice build up was most likely the cause of the vibrations.